Question

Help please!!! steps would be nice
The board of directors of a company knows that the probability that the carbon emission from the company’s manufacturing unit is exceeding the permissible level is 35%. A consultant is hired to use a carbon footprint calculator to test for the emission level. The accuracy of this test is said to be 85%.
You have this additional information: the test reported that the carbon emission from the manufacturing unit is well within the permissible level. What is the probability that the emission is within the permissible level, given the outcome of the test?

Answer 1

this problem is rather poorly stated because it does not define what they mean by 'accuracy'. if we take it to mean that, if emissions are excessive, there is an 85% the test will say so, and if emissions are not, the test will correctly indicate that with probability 85%/
do you think that is a fair assumption to make here?

Answer 2

yes

Answer 3

i feel like there is not enough information its confusing

Answer 4

there is enough information if we make this assumption, but the answer will surprise you. I won't give it to you, but i will try to get you going on how to find it.
let
\(P(\text{excessive levels of emissions})=P(A)=0.35\)
\(P(\text{testing positive})=P(B)\)
we are given with the accuracy statement that
\[P(B|A)=0.85\]\[P(B^C|A^C)=0.85\]
is this making sense so far?

Answer 5

so would i write it like this 35/85

Answer 6

no, division has nothing to do with it. the notation for condition probabilities P(A|B) mean 'the probability of A given B'
you seem to think it has something to do with division, so clearly you don't know this notation. You have been studying condition probability i assume though, correct?

Answer 7

yes and my teacher said I need to convert the percentage to a fraction

Answer 8

well i guess that's one way to do it, though i don't see the point. i don't know which part she meant, but i have to assume she meant that if the probability of something happening is 85/100, then the probability of it not happening is 15/100....
i don't see why you can't just say 0.85 and 0.15 though

Answer 9

do you know baye's rule?

Answer 10

Bayes therom the difference between event 1 and event 2

Answer 11

no, bayes theorem tell you how to get from P(A|B) to P(B|A)
how about the total probability theorem? do you know that?

Answer 12

that is used to figure out what the probability is like if you roll a dice what is the probability you will get a 3 1/6

Answer 13

probability of a random event

Answer 14

yes it can be, but it can also use conditional probabilities to determine the likelyhood of an event independent of conditions
P(B)=P(A)P(B|A)+P(A)P(~B|A)

-- '~B' means 'not B'

Answer 15

i'm trying to figure out what tools you have to solve the problem, because it seems like all the ways i know are pretty foreign to you

Answer 16

if i draw a diagram like so does this make senseis this something you've seen?

Answer 17

No I haven't learned this yet. Im going to go back and see if its in the book thanks

Answer 18

ok, sorry i couldn't find a tool you could use. Good luck, i'll be here if this starts making more sense

Answer 19

thanks

Answer 20

whats the answer to this